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An important and fundamental issue in designing structured P2P systems is the tradeoff between the number of logical links and the number of hops. This paper presents K-Chord (KC), a flexible protocol based on Chord and the idea of proportional search. We conduct an in-depth study on KC. Let D denote any given number, in order to guarantee that each query can be resolved in 0(D) hops, it is necessary and sufficient to maintain Omega(D(n1/D - 1)) links on each node in KC, where n is the number of nodes in the system. The performances of KC have been evaluated using both theoretical analysis and simulation.